Let us write \(W_n=G(2,1,n)\)  for the Weyl group of type \(B_n\)  (or \(C_n\) ). Let \(\mathcal {H}^{rat}_{c_1,c_2}(W_n)\)  denote the rational Cherednik algebra of \(W_n\) , with parameter \(c_1\)  (resp. \(c_2\) ) assigned to the reflections associated to hyperplanes \(z_i=z_j\)  (resp. \(z_i=0\) ), defined by Etingof–Ginzburg [1]}. Let \(\Omega ^{c_1,c_2}(n)\)  denote the number of finite dimensional simple modules of \(\mathcal {H}^{rat}_{c_1,c_2}(W_n)\) . It is known [2]} (private communication with E. Norton) that
\( \sum _{n\ge 0} \Omega ^{\frac{1}{2},1}(n) x^n= \prod _{n\ge 1} \frac{1+x^{2n} }{1-x^{2n} },\) 
